∠e and ∠f are vertical angles with m∠e=9x+12 and m∠f=3x+24 .

what is the value of x?

vertical angles are always congruent so the E & F have to have the same end result

therefore we have to find a single x value that makes E & F equal each other

okay so we can set the equations to equal each other and solve for x

so:

9x + 12 = 3x + 24

we need to get all the x terms to one side so let's subtract 12 from both sides

now we have

9x = 3x + 12

now let's subtract 3x from both sides to get

6x = 12

we can solve for x like normal now

x = 2

now to check this and see if it is accurate we plug in 2 for x in both equations

E = 9(2) + 12

E = 30

F = 3(2) + 24

F = 30

because they both got the same answer, we know that x = 2 is the right answer